Abstract

Proximal smoothness and the exterior sphere condition are compared. It is shown via examples that these two properties are not necessarily equivalent, and geometric conditions are provided under which the equivalence holds.

Author information

Contact details are reproduced from the original publication and may be historical.

Chadi Nour

Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon

cnour@lau.edu.lb

Ron J. Stern

Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada

stern@mathstat.concordia.ca

Jean Takche

Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus, Lebanon

jtakchi@lau.edu.lb

Keywords

  • Proximal smoothness
  • interior and exterior sphere conditions
  • wedged sets
  • proximal analysis
  • nonsmooth analysis

Suggested citation

C. Nour, R. J. Stern, J. Takche. “Proximal Smoothness and the Exterior Sphere Condition.” Journal of Convex Analysis 16 (2009), No. 2, 501–514.

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press.